Transparency 6-3. 5-Minute Check on Lesson 6-2. Determine whether the triangles are similar. Justify your answer. The quadrilaterals are similar. Write a similarity statement and find the scale factor of the larger to the smaller quadrilateral. The triangles are similar. Find x and y.
5-Minute Check on Lesson 6-2
Yes: corresponding angles corresponding sides have same proportion
ABCD ~ HGFE
Scale factor = 2:3
x = 8.5, y = 9.5
Standardized Test Practice:
Two rectangles are similar
Two right triangles are similar
Two acute triangles are similar
Two isosceles right triangles are similar
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If the measures of two sides of a triangle are proportional to the measures of two corresponding side of another triangle and the included angles are congruent, then the triangles are similar
In the figure, AB // DC, BE = 27, DE= 45, AE = 21, and CE = 35. Determine which triangles in the figure are similar.
Since AB ‖ DC, then BAC DCE by the Alternate Interior Angles Theorem.
Vertical angles are congruent, so BAE DEC.
Answer: Therefore, by the AA Similarity Theorem, ∆ABE ∆CDE
INDIRECT MEASUREMENT Josh wanted to measure the height of the Sears Tower in Chicago. He used a 12-foot light pole and measured its shadow at 1 P.M. The length of the shadow was 2 feet. Then he measured the length of the Sears Tower’s shadow and it was 242 feet at that time. What is the height of the Sears Tower?
Assuming that the sun’s rays form similar ∆s, the following proportion can be written.
Now substitute the known values and let x be the height of the Sears Tower.
Answer: The Sears Tower is 1452 feet tall.
INDIRECT MEASUREMENTOn her trip along the East coast, Jennie stops to look at the tallest lighthouse in the U.S. located at Cape Hatteras, North Carolina. At that particular time of day, Jennie measures her shadow to be 1 feet 6 inches in length and the length of
the shadow of the lighthouse to be 53 feet 6 inches. Jennie knows that her height is 5 feet 6 inches. What is the height of the Cape Hatteras lighthouse to the nearest foot?
Answer: 196 ft
Similar Triangles (determine if similar and list in proper order)
x + 7
x - 12
x + 2
y + 1
x + 1
x - 3
x + 3
11x - 2